I wouldn't bother with suing. It costs money, takes time, and isn't about personality but whether what they actually did, caused damage. It just sounds like they didn't do anything for you, not that they did it "wrong".

I'd look for a doctor who understands you and your problems and work with him/her. But doctors don't know everything; if you don't think a doctor has an answer that suits you, go find one that does. One has to work together with one's doctor to get a good doctor/patient "fit". Maybe the second doctor didn't know anything about mental illness and didn't think he could help you. But calling you names or not responding to letters aren't suing offenses, they just mean those doctors aren't ones you want to see.

Suing can work against one too, if one does it a lot; one could get a name for suing and doctors wouldn't want to work with one (and they don't have to). I concentrate on my own issues rather than any doctor's. If a doctor doesn't suit me, I find one whose ideas and methods more closely agree with mine.

I had a major medical scare several years ago and a lot of mistakes were made but most of them are only noticeable in hindsight, once what was wrong with me was fully known. Of 4+ doctors I had to work closely with over six months, I almost sued one but did not because it wouldn't have helped me any. My therapist recommended courses of action I also did not take, to help others seeing that doctor so the doctor could "correct" her practices and not endanger others as she had me but that would have been a lot of work for me to do for others and I wanted to concentrate on getting better at that time (I almost died a couple times).